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Remember class: The volume of a rectangular prism is calculated by multiplying length × width × height (V = l × w × h). Think of it as counting how many cubic units fill up the entire shape!

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Rectangular prisms are everywhere! Think about a shoe box, a cereal box, or your classroom. Understanding volume helps us know how much space these objects take up or how much they can hold inside.

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A toy box has a length of 12 inches, width of 8 inches, and height of 6 inches. Calculate its volume. Remember to show your work: 12 × 8 × 6 = ??? cubic inches

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An aquarium is 24 inches long, 12 inches wide, and 18 inches high. How many cubic inches of water can it hold when full? Use the volume formula!

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Your family is moving and has a box that is 15 inches long, 10 inches wide, and 9 inches high. What is the volume of this moving box?

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Practice calculating volume with this interactive tool! Input different dimensions and see how the volume changes. Great for checking your work!

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Rectangular Prism Shape

l = length
w = width
h = height
d = diagonal
S tot = total surface area
S lat = lateral surface area
S top = top surface area
S bot = bottom surface area
V = volume

Calculator Use

Enter any 3 variables for a rectangular prism into this online calculator to calculate the other 3 unknown variables. A cube is a special case where l = w = h for a rectangular prism.

Units: Note that units are shown for convenience but do not affect the calculations. The units are in place to give an indication of the order of the results such as ft, ft ² or ft ³. For example, if you are starting with mm and you know h, l and w in mm, your calculations will result with d in mm, S in mm ² and V in mm ³.

Formulas for a rectangular prism:

Volume of Rectangular Prism:

Surface Area of Rectangular Prism:

Space Diagonal of Rectangular Prism: (similar to thedistance between 2 points)

A cube is a special case where l = w = h. So you can find the volume of a cube or surface area of a cube by setting these values equal to each other.

Calculations for a rectangular prism:

1. Given the length, width and height find the volume, surface area and diagonal of a rectangular prism

2. Given the surface area, length and width find the height, volume and diagonal of a rectangular prism

3. Given the volume, length and width find the height, surface area, and diagonal of a rectangular prism

4. Given the diagonal, length and width find the height, volume and surface area of a rectangular prism

For more information on cuboids see: Weisstein, Eric W. "Cuboid." From MathWorld--A Wolfram Web Resource, Cuboid.

Last updated: October 4, 2023

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Calculator online for a rectangular prism. Cuboid Calculator. Calculate the unknown defining surface areas, lengths, widths, heights, and volume of a rectangular prism with any 3 known variables. Online calculators and formulas for a prism and other geometry problems.

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Hey students! Try this fun game where you can practice finding volumes of different rectangular prisms. See how many you can solve correctly!

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Volume Formula for Rectangular Prisms Math Games

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Show Fractional Values with a Line Plot math games, based on CCSS & state standards. Learn to make a line plot to display a data set in fractions of a unit.